How is LCM related to GCF?

LCM and GCF are connected: LCM(a,b) × GCF(a,b) = a × b. So if you know the GCF, you can find the LCM quickly. For 12 and 18: GCF = 6, so LCM = (12 × 18) / 6 = 216 / 6 = 36.

Why do I need LCM for adding fractions?

To add fractions, they need the same denominator. The LCM of the denominators (called LCD, Least Common Denominator) is the smallest such denominator. For 1/4 + 1/6, LCD = LCM(4,6) = 12. Convert: 3/12 + 2/12 = 5/12.

What is the LCM when one number divides the other?

When one number divides evenly into the other, the LCM is the larger number. For example, LCM(4, 8) = 8 because 4 divides into 8. This makes sense: 8 is already divisible by both 4 and 8.

How do I find LCM of more than two numbers?

Find the LCM of the first two, then find the LCM of that result with the third number, and so on. Or use prime factorization: take the highest power of each prime that appears in any number. LCM(4,6,9) = 2² × 3² = 36.

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Solution Method

LCM (Least Common Multiple)

GCD (Greatest Common Divisor)

calculators.lcm.stepByStepPrimeFactorization

calculators.lcm.step1PrimeFactorize

12 = 2^2 × 3

18 = 2 × 3^2

calculators.lcm.step2HighestPower

LCM = 2^2 × 3^2 = 36

calculators.lcm.step3LowestPower

GCD = 2 × 3 = 6

Prime Factor Visualization

2^2((shared))

3^2((shared))

LCM & GCD Relationship

For Two Numbers

LCM(a,b) × GCD(a,b) = a × b

Coprime Numbers

calculators.lcm.coprimeFormula

calculators.lcm.whenToUseLCM

calculators.lcm.addingFractions

calculators.lcm.addingFractionsEx

calculators.lcm.scheduling

calculators.lcm.schedulingEx

calculators.lcm.gearRatios

calculators.lcm.gearRatiosEx

calculators.lcm.timeCycles

calculators.lcm.timeCyclesEx

出典と方法論

公式： LCM(a,b) = |a × b| / GCD(a,b)

Least common multiple using GCD

出典： Number theory fundamentals

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How to Use the LCM Calculator

The LCM (Least Common Multiple) calculator finds the smallest number that is a multiple of two or more numbers. See the solution using multiple methods: prime factorization, listing multiples, and the division method.

What is LCM?

The Least Common Multiple is the smallest positive number that is divisible by all the given numbers:

LCM(4, 6) = 12 because 12 is the smallest number divisible by both 4 and 6.

Method 1: Prime Factorization

Find the prime factorization of each number
Take the highest power of each prime
Multiply them together

Example: LCM(12, 18)
12 = 2² × 3
18 = 2 × 3²
LCM = 2² × 3² = 4 × 9 = 36

Method 2: Listing Multiples

List multiples of each number until you find a common one:

Multiples of 4: 4, 8, 12, 16, 20...
Multiples of 6: 6, 12, 18, 24...
LCM = 12

Method 3: Using GCF

The LCM and GCF are related:

LCM(a, b) = (a × b) / GCF(a, b)

Real-World Applications

Adding fractions: Finding a common denominator
Scheduling: When events coincide again
Gear ratios: Finding full rotation cycles

Related Calculators

For finding the GCF, use our GCF calculator. For fraction operations, try our fraction calculator.

よくある質問

The Least Common Multiple (LCM) is the smallest positive number that both numbers divide into evenly. For example, LCM(4, 6) = 12 because 12 is the smallest number divisible by both 4 and 6 (12÷4=3, 12÷6=2).